Well, you've got lots of choices. The 87-93 mustang might cost slgihtly mor than $2k to start with, but parts for it are a lot cheaper than many other cars. There's also no shartage of parts/shops/knowledgeable people when it comes to them. Same goes for the older mustangs from the 60s and 70s. You can probably find one under $2k, but it'll be more work to get it in decent shape.
The bug is a good choice; cheap and lots of parts avaialble, but it's air-cooled which means that not everything in there will be applciable to most other cars.
Then there's tons of old chevy's around. There are plenty of parts for chevelles and such around, kinda like the mustang.
You could also look into trucks. The ford F-series goes WAY back and you can build some pretty cool old trucks with them.
Then there's also the imports, but i don't know as much about them.
Keep in mind how much work this is goig to be.
Here are some pics from when I did my engine swap All we did was pull out the old motor, assemble the new one, and drop it back in the car, and that was 3 weekends and about $4000. Body and paint work takes a lot longer than mechanical work, and you'll also have the interior to deal with. You'll want to pick a car that you can find new seats and things for if the ones you get are torn up.